There are several different ways to test the velocity birefringence induced by \({\cal W}_1 - {\cal G}_1\)  in spatial covariant gravity. In ref. [1]}, the velocity birefringence has been constrained by comparing the arrival times of GW170817 and GRB170817a, which gives
\(|{\cal W}_1 - {\cal G}_1| \lesssim 10^{-11} \; {\rm km}. \) 
